共查询到20条相似文献,搜索用时 31 毫秒
1.
Wojciech Jab?oński 《Journal of Mathematical Analysis and Applications》2005,312(2):527-534
Assume that and are uniformly continuous functions, where D1,D2⊂X are nonempty open and arc-connected subsets of a real normed space X. We prove that then either f and g are affine functions, that is f(x)=x∗(x)+a and g(x)=x∗(x)+b with some x∗∈X∗ and a,b∈R or the algebraic sum of graphs of functions f and g has a nonempty interior in a product space X×R treated as a normed space with a norm . 相似文献
2.
Let G∗,G be finite abelian groups with nontrivial homomorphism group . Let Ψ be a non-empty subset of . Let DΨ(G) denote the minimal integer, such that any sequence over G∗ of length DΨ(G) must contain a nontrivial subsequence s1,…,sr, such that for some ψi∈Ψ. Let EΨ(G) denote the minimal integer such that any sequence over G∗ of length EΨ(G) must contain a nontrivial subsequence of length |G|,s1,…,s|G|, such that for some ψi∈Ψ. In this paper, we show that EΨ(G)=|G|+DΨ(G)−1. 相似文献
3.
Enkelejd Hashorva 《Journal of multivariate analysis》2010,101(4):926-935
In this paper we consider elliptical random vectors in Rd,d≥2 with stochastic representation , where R is a positive random radius independent of the random vector which is uniformly distributed on the unit sphere of Rd and A∈Rd×d is a given matrix. Denote by ‖⋅‖ the Euclidean norm in Rd, and let F be the distribution function of R. The main result of this paper is an asymptotic expansion of the probability for F in the Gumbel or the Weibull max-domain of attraction. In the special case that is a mean zero Gaussian random vector our result coincides with the one derived in Hüsler et al. (2002) [1]. 相似文献
4.
Zhichun Zhai 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2611-2630
Let be the space of solutions to the parabolic equation having finite norm. We characterize nonnegative Radon measures μ on having the property , 1≤p≤q<∞, whenever . Meanwhile, denoting by v(t,x) the solution of the above equation with Cauchy data v0(x), we characterize nonnegative Radon measures μ on satisfying , β∈(0,n), p∈[1,n/β], q∈(0,∞). Moreover, we obtain the decay of v(t,x), an isocapacitary inequality and a trace inequality. 相似文献
5.
Let V(x) be a non-negative, bounded potential in RN, N?3 and p supercritical, . We look for positive solutions of the standing-wave nonlinear Schrödinger equation Δu−V(x)u+up=0 in RN, with u(x)→0 as |x|→+∞. We prove that if V(x)=o(−2|x|) as |x|→+∞, then for N?4 and this problem admits a continuum of solutions. If in addition we have, for instance, V(x)=O(|x|−μ) with μ>N, then this result still holds provided that N?3 and . Other conditions for solvability, involving behavior of V at ∞, are also provided. 相似文献
6.
Mei-Chu Chang 《Journal of Functional Analysis》2007,247(2):417-437
Let p,q∈R such that 1<p<2 and . Define
(∗) 相似文献
7.
We consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where 0∈Ω is a smooth bounded domain in RN, N?4, , is the critical Sobolev exponent, f(x,⋅) has subcritical growth at infinity, K(x)>0 is continuous. We prove the existence of sign-changing solutions under different assumptions when Ω is a usual domain and a symmetric domain, respectively. 相似文献
8.
M. Bhakta 《Journal of Differential Equations》2009,247(1):119-139
We study the regularity, Palais-Smale characterization and existence/nonexistence of solutions of the Hardy-Sobolev-Maz'ya equation in a bounded domain in RN where x∈RN is denoted as x=(y,z)∈Rk×RN−k and . We show different behaviors of PS sequences depending on t=0 or t>0. 相似文献
9.
Quoc-Phong Vu 《Journal of Mathematical Analysis and Applications》2007,334(1):487-501
We study properties of solutions of the evolution equation , where B is a closable operator on the space AP(R,H) of almost periodic functions with values in a Hilbert space H such that B commutes with translations. The operator B generates a family of closed operators on H such that (whenever eiλtx∈D(B)). For a closed subset Λ⊂R, we prove that the following properties (i) and (ii) are equivalent: (i) for every function f∈AP(R,H) such that σ(f)⊆Λ, there exists a unique mild solution u∈AP(R,H) of Eq. (∗) such that σ(u)⊆Λ; (ii) is invertible for all λ∈Λ and . 相似文献
10.
Bertrand Lemaire 《Discrete Mathematics》2009,309(12):3793-3810
In this paper, we study the binary relations R on a nonempty N∗-set A which are h-independent and h-positive (cf. the introduction below). They are called homothetic positive orders. Denote by B the set of intervals of R having the form [r,+∞[ with 0<r≤+∞ or ]q,∞[ with q∈Q≥0. It is a Q>0-set endowed with a binary relation > extending the usual one on R>0 (identified with a subset of B via the map r?[r,+∞[). We first prove that there exists a unique map ΦR:A×A→B such that (for all and all ) we have Φ(mx,ny)=mn−1⋅Φ(x,y) and . Then we give a characterization of the homothetic positive orders R on A such that there exist two morphisms of N∗-sets satisfying . They are called generalized homothetic biorders. Moreover, if we impose some natural conditions on the sets u1(A) and u2(A), the representation (u1,u2) is “uniquely” determined by R. For a generalized homothetic biorder R on A, the binary relation R1 on A defined by is a generalized homothetic weak order; i.e. there exists a morphism of N∗-sets u:A→B such that (for all ) we have . As we did in [B. Lemaire, M. Le Menestrel, Homothetic interval orders, Discrete Math. 306 (2006) 1669-1683] for homothetic interval orders, we also write “the” representation (u1,u2) of R in terms of u and a twisting factor. 相似文献
11.
We consider the following question: given A∈SL(2,R), which potentials q for the second order Sturm-Liouville problem have A as its Floquet multiplier? More precisely, define the monodromy map μ taking a potential q∈L2([0,2π]) to , the lift to the universal cover of SL(2,R) of the fundamental matrix map ,
12.
13.
Lei Zhang 《Journal of Differential Equations》2009,247(5):1334-1353
We consider positive solutions of on B1 (n?5) where μ and K>0 are smooth functions on B1. If K is very sub-harmonic at each critical point of K in B2/3 and the maximum of u in is comparable to its maximum over , then all positive solutions are uniformly bounded on . As an application, a priori estimate for solutions of equations defined on Sn is derived. 相似文献
14.
15.
Let s∈R, τ∈[0,∞), p∈(1,∞) and q∈(1,∞]. In this paper, we introduce a new class of function spaces which unify and generalize the Triebel-Lizorkin spaces with both p∈(1,∞) and p=∞ and Q spaces. By establishing the Carleson measure characterization of Q space, we then determine the relationship between Triebel-Lizorkin spaces and Q spaces, which answers a question posed by Dafni and Xiao in [G. Dafni, J. Xiao, Some new tent spaces and duality theorem for fractional Carleson measures and Qα(Rn), J. Funct. Anal. 208 (2004) 377-422]. Moreover, via the Hausdorff capacity, we introduce a new class of tent spaces and determine their dual spaces , where s∈R, p,q∈[1,∞), max{p,q}>1, , and t′ denotes the conjugate index of t∈(1,∞); as an application of this, we further introduce certain Hardy-Hausdorff spaces and prove that the dual space of is just when p,q∈(1,∞). 相似文献
16.
Dongsheng Kang Shuangjie Peng 《Journal of Mathematical Analysis and Applications》2004,291(2):488-499
Let be a smooth bounded domain such that 0∈Ω, N?7, 0?s<2, 2∗(s)=2(N−s)/(N−2). We prove the existence of sign-changing solutions for the singular critical problem −Δu−μ(u/|x|2)=(|u|2∗(s)−2/|x|s)u+λu with Dirichlet boundary condition on Ω for suitable positive parameters λ and μ. 相似文献
17.
Zhi-Hong Sun 《Journal of Number Theory》2007,124(1):62-104
Let p>3 be a prime, u,v,d∈Z, gcd(u,v)=1, p?u2−dv2 and , where is the Legendre symbol. In the paper we mainly determine the value of by expressing p in terms of appropriate binary quadratic forms. As applications, for we obtain a general criterion for and a criterion for εd to be a cubic residue of p, where εd is the fundamental unit of the quadratic field . We also give a general criterion for , where {Un} is the Lucas sequence defined by U0=0, U1=1 and Un+1=PUn−QUn−1 (n?1). Furthermore, we establish a general result to illustrate the connections between cubic congruences and binary quadratic forms. 相似文献
18.
Maitere Aguerrea 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(6):2753-1889
We establish the existence of a continuous family of fast positive wavefronts u(t,x)=?(x+ct), ?(−∞)=0, ?(+∞)=κ, for the non-local delayed reaction-diffusion equation . Here 0 and κ>0 are fixed points of g∈C2(R+,R+) and the non-negative K is such that is finite for every real λ. We also prove that the fast wavefronts are non-monotone if . 相似文献
19.
We consider an inclusion B⊆M of finite von Neumann algebras satisfying B′∩M⊆B. A partial isometry v∈M is called a groupoid normalizer if vBv∗,v∗Bv⊆B. Given two such inclusions Bi⊆Mi, i=1,2, we find approximations to the groupoid normalizers of in , from which we deduce that the von Neumann algebra generated by the groupoid normalizers of the tensor product is equal to the tensor product of the von Neumann algebras generated by the groupoid normalizers. Examples are given to show that this can fail without the hypothesis , i=1,2. We also prove a parallel result where the groupoid normalizers are replaced by the intertwiners, those partial isometries v∈M satisfying vBv∗⊆B and v∗v,vv∗∈B. 相似文献
20.
Mohammad Javaheri 《Journal of Mathematical Analysis and Applications》2010,361(2):332-337
Let γ:[0,1]→2[0,1] be a continuous curve such that γ(0)=(0,0), γ(1)=(1,1), and γ(t)∈2(0,1) for all t∈(0,1). We prove that, for each n∈N, there exists a sequence of points Ai, 0?i?n+1, on γ such that A0=(0,0), An+1=(1,1), and the sequences and , 0?i?n, are positive and the same up to order, where π1, π2 are projections on the axes. 相似文献